Details

sample193.0ms

Algorithm

intervals

Results

92.0ms	98×	body	2560	valid
38.0ms	80×	body	1280	valid
18.0ms	284×	body	80	nan
14.0ms	44×	body	640	valid
4.0ms	17×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	6×	body	80	valid

simplify5.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	20	14
2	43	14
3	84	14
4	155	14
5	241	14
6	330	14
7	482	14
8	1107	14
done	5001	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- 1.0 (* 5.0 (* v v)))
0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

46.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
15.0ms	(- 1.0 (* 5.0 (* v v)))
22.0ms	(* 5.0 (* v v))
2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
81.0ms	(- 1.0 (* 5.0 (* v v)))
39.0ms	(* 5.0 (* v v))
5.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify3.1s

Counts

101 → 101

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	163	1547
1	377	1484
2	1169	1356
3	4100	1349
done	5000	1349

prune332.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* v v) 1.0)
0.0b	(/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0))
0.1b	(* (* 5.0 5.0) (pow v 4))
0.4b	(acos (/ (/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0)) (- (* v v) 1.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
18×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-cbrt-cube`
9×	`times-frac` `prod-exp`
7×	`associate-r`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u`
3×	`prod-diff` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `sqr-pow`
1×	`cbrt-undiv` `acos-asin` `sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `div-exp` `associate-l` `clear-num` `*-commutative` `flip--` `div-inv` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

10.0ms	(- (* v v) 1.0)
5.0ms	(/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0))
36.0ms	(* (* 5.0 5.0) (pow v 4))
1.0ms	(acos (/ (/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0)) (- (* v v) 1.0)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* v v) 1.0)
249.0ms	(/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0))
70.0ms	(* (* 5.0 5.0) (pow v 4))
7.0ms	(acos (/ (/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0)) (- (* v v) 1.0)))

simplify3.6s

Counts

99 → 99

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	183	1791
1	372	1709
2	1014	1535
3	3882	1518
done	5000	1518

prune512.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ PI 2) (asin (/ (/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0)) (- (* v v) 1.0))))
0.0b	(/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0))
0.1b	(* (* 5.0 5.0) (pow v 4))
0.4b	(asin (/ (/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0)) (- (* v v) 1.0)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
46×	`times-frac`
39×	`prod-diff`
19×	`add-exp-log`
13×	`fma-neg`
11×	`add-cbrt-cube`
9×	`prod-exp`
7×	`associate-r`
6×	`add-log-exp`
5×	`div-inv`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u`
3×	`associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`pow-to-exp` `asin-acos` `pow-exp` `difference-of-squares` `sqr-pow`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `associate-l` `clear-num` `*-commutative` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 138

Calls

4 calls:

38.0ms	(- (/ PI 2) (asin (/ (/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0)) (- (* v v) 1.0))))
10.0ms	(/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0))
25.0ms	(* (* 5.0 5.0) (pow v 4))
1.0ms	(asin (/ (/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0)) (- (* v v) 1.0)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (/ PI 2) (asin (/ (/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0)) (- (* v v) 1.0))))
286.0ms	(/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0))
48.0ms	(* (* 5.0 5.0) (pow v 4))
8.0ms	(asin (/ (/ (fma 1.0 1.0 (- (* (* 5.0 5.0) (pow v 4)))) (fma (* 5.0 v) v 1.0)) (- (* v v) 1.0)))

simplify3.4s

Counts

150 → 150

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	247	9544
1	509	6235
2	1251	4953
3	4129	3803
done	5000	3802

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

11.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series776.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
204.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
172.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
174.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify5.3s

Counts

93 → 93

Iterations

Useful iterations: 4 (2.9s)

Iter	Nodes	Cost
0	65	2636
1	113	2441
2	309	1957
3	1034	1887
4	4523	1867
done	5001	1867

prune278.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes193.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	29
1	26	29
2	31	29
done	31	29

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.4s	3024×	body	2560	valid
1.2s	2473×	body	1280	valid
879.0ms	1240×	body	640	valid
510.0ms	8253×	body	80	nan
118.0ms	586×	body	320	valid
67.0ms	472×	body	160	valid
17.0ms	205×	body	80	valid